Persistence and patience paid of against a stubborn Torquay side that were reduced to ten men when Brian Saah was dismissed in the first half. A late strike from Alan Connell proved to be the decider five minutes from time.
City started brightly and inside the first 2 minutes, visiting stopper Michael Poke was being sternly tested; Wells' cross was guided towards goal by the head of James Hanson but Poke pulled off a superb save to prevent him scoring his third goal in three games.
Hanson was getting large amounts of joy in the air and Gary Jones' delivery was knocked down by the big frontman and Garry Thompson was unlucky when his hopeful overhead shot dropped narrowly over the bar with Poke a spectator.
The Bantams were clearly dominant early on and went in constant search of an early goal, Nahki Wells was allowed the space to run into and after finding half a yard on a Torquay defender he lashed a shot narrowly over the bar.
On 35 minutes, Torquay's hopes of leaving Bradford with a result took a turn for the worse when skipper Brian Saah was given a straight red card by referee Darren Bond for an elbow on James Meredith.
Surprisingly it was United who came the closest to scoring soon after Saah's dismissal; Rene Howe's flick on found early substitute Niall Thompson who curled a low shot back off the far post with Duke beaten.
City also tested the strength of the goal frame just before half time; Wells' hanging cross was inviting and James Hanson headed towards goal but the ball came back off the crossbar from only a few yards out.
Parkinson's men carried on bombarding Torquay's area and Rory McArdle's header from Gary Jones' set piece looped narrowly wide of the target and another one of Jones' freekick deliveries landed on the head of McHugh but the header was straight at Michael Poke, either side of him and the deadlock would surely have been broken.
Leading scorer Nahki Wells then tried his luck; Will Atkinson cleverly picked him out in the area and his fierce angled drive was pushed onto the post by Poke to further frustrate The Bantams.
Substitute Blair Turgott was having an instant impact on the game and he almost grabbed himself a wonder goal when he produced a dazzling run forward, taking on several players before lashing a shot from the edge of the area narrowly wide of the target.
With only 5 minutes of normal time remaining City took the lead; Nahki Wells' cross from the left hand side evaded a crowd of players and Alan Connell hit a first time strike that rifled into the top corner in front of the jubilant Kop to hand The Bantams all three points.
Wells nearly added gloss to the scoreline with a goal of his own when he raced clear; his firm strike was pushed over the bar by Poke to prevent his side from conceding twice in as many minutes.
City had left it late, but finally unlocked their resilient opponents with a late strike to move up to 4th place in League 2 ahead of the upcoming Capital One Cup Quarter Final against Arsenal.